Airfoil Shape for a Turbine Rotor Blade

ABSTRACT

A turbine rotor blade is provided including an airfoil having an airfoil shape. The turbine rotor blade airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.

FIELD

The present invention relates to an airfoil for a turbine rotor blade ofa stage of a turbine and particularly relates to a shape defining aprofile for an airfoil of a turbine rotor blade.

BACKGROUND

Some aircraft and/or power plant systems, for example certain jetaircraft, nuclear, simple cycle and combined cycle power plant systems,employ turbines (also referred to as turbomachines) in their design andoperation. Some of these turbines employ airfoils (e.g., turbine rotorblades, blades, airfoils, etc.) which during operation are exposed tofluid flows. These airfoils are configured to aerodynamically interactwith the fluid flows and generate energy (e.g., creating thrust, turningkinetic energy to mechanical energy, thermal energy to mechanicalenergy, etc.) from these fluid flows as part of power generation. As aresult of this interaction and conversion, the aerodynamiccharacteristics and losses of these airfoils have an impact on systemand turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION

Aspects and advantages are set forth below in the following description,or may be obvious from the description, or may be learned throughpractice.

An aspect of the present invention may be embodied by a turbine rotorblade including an airfoil having an airfoil shape, the airfoil having anominal profile substantially in accordance with Cartesian coordinatevalues of X, Y and Z set forth in Table I wherein the Cartesiancoordinate values of X, Y and Z are non-dimensional values from 0% to100% convertible to dimensional distances in inches by multiplying theCartesian coordinate values of X, Y and Z by a height of the airfoil ininches, and wherein X and Y are distances in inches which, whenconnected by smooth continuing arcs, define airfoil profile sections ateach distance Z, the airfoil profile sections at Z distances beingjoined smoothly with one another to form a complete airfoil shape.

An aspect of the present invention may be embodied in a turbine rotorblade including an airfoil having a suction-side uncoated nominalairfoil profile substantially in accordance with suction-side Cartesiancoordinate values of X, Y and Z set forth in Table I wherein theCartesian coordinate values of X, Y and Z are non-dimensional valuesfrom 0% to 100% convertible to dimensional distances in inches bymultiplying the Cartesian coordinate values of X, Y and Z by a height ofthe airfoil in inches, and wherein X and Y are distances in incheswhich, when connected by smooth continuing arcs, define airfoil profilesections at each Z distance, the airfoil profile sections at the Zdistances being joined smoothly with one another to form a completesuction-side airfoil shape, the X, Y and Z distances being scalable as afunction of the same constant or number to provide a scaled-up orscaled-down airfoil.

An aspect of the present invention may be embodied in a turbinecomprising a turbine wheel having a plurality of turbine rotor blades,each of the turbine rotor blades including an airfoil having asuction-side airfoil shape, the airfoil having a nominal profilesubstantially in accordance with suction-side Cartesian coordinatevalues of X, Y and Z set forth in Table I wherein the Cartesiancoordinate values of X, Y and Z are non-dimensional values from 0% to100% convertible to dimensional distances by multiplying the Cartesiancoordinate values of X, Y and Z by a height of the airfoil, and whereinX and Y are distances which, when connected by smooth continuing arcs,define airfoil profile sections at each Z distance, the airfoil profilesections at the Z distances being joined smoothly with one another toform a complete suction-side airfoil shape.

Those of ordinary skill in the art will better appreciate the featuresand aspects of such embodiments, and others, upon review of thespecification.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of various embodiments, including thebest mode thereof to one skilled in the art, is set forth moreparticularly in the remainder of the specification, including referenceto the accompanying figures, in which:

FIG. 1 is a schematic representation of an exemplary turbine havingmultiple stages with each stage including alternating rows of turbinerotor blades and stationary vanes or nozzles according to at least oneembodiment of the present disclosure; and

FIG. 2 is a perspective view of a turbine rotor blade according to atleast one embodiment of the present disclosure.

DETAILED DESCRIPTION

Referring now to the drawings, particularly to FIG. 1, there isillustrated an exemplary turbine 10 of a gas turbine 12 including aplurality of turbine stages arranged in serial flow order. Each stage ofthe turbine includes a row of turbine nozzles or vanes disposed axiallyadjacent to a corresponding row of turbine rotor blades. Four stages areillustrated in FIG. 1. The exact number of stages of the turbine 10 is achoice of engineering design, and may be more or less than the fourstages illustrated in FIG. 1. The four stages are merely exemplary ofone turbine design, and are not intended to limit the presently claimedturbine rotor blade in any manner.

The first stage comprises a plurality of turbine nozzles or vanes 100and a plurality of turbine rotor blades 150. The turbine nozzles 100 areannularly arranged about an axis of a turbine rotor 14. The turbinerotor blades 150 are annularly arranged about and coupled to the turbinerotor 14. A second stage of the turbine 12 includes a plurality ofturbine nozzles 200 annularly arranged about the axis of the turbinerotor 14 and a plurality of turbine rotor blades 250 annularly arrangedabout and coupled to the turbine rotor 14. The turbine nozzles 200 maybe coupled to a casing 16 of the turbine 12.

As shown in FIG. 1, a third stage of the turbine 12 includes a pluralityof turbine nozzles 300 annularly arranged about the axis of the turbinerotor 14 and a plurality of turbine rotor blades 350 annularly arrangedabout and coupled to the turbine rotor 14. The turbine nozzles 300 maybe coupled to the casing 16 of the turbine 12. In particularembodiments, the turbine 12 includes a fourth stage which includesplurality of turbine nozzles 400 annularly arranged about the axis ofthe turbine rotor 14 and a plurality of turbine rotor blades 450annularly arranged about and coupled to the turbine rotor 14. The fourthstage turbine nozzles 400 may be coupled to the casing 16 of the turbine12.

It will be appreciated that the turbine nozzles 100, 200, 300 and 400and turbine rotor blades 150, 250, 350 and 450 are disposed or at leastpartially disposed within a hot gas path 18 of the turbine 12. Thevarious stages of the turbine 10 at least partially define the hot gaspath 18 through which combustion gases, as indicated by arrows 20, flowduring operation of the gas turbine 12.

FIG. 2 provides a perspective view of an exemplary turbine rotor blade50 as may be incorporated in any stage of the turbine 12. For example,in one embodiment the turbine rotor blade 50 is representative of aturbine rotor blade 150 of the plurality of turbine rotor blades 150 ofthe first stage. As shown in FIG. 2, the turbine rotor blade 50 includesan airfoil 52 having a pressure-side wall 54 and an opposingsuction-side wall 56. The pressure-side wall 54 and the suction-sidewall 56 meet or intersect at a leading edge 58 and a trailing edge 60 ofthe airfoil 52. A chord line 62 extends between the leading edge 58 andthe trailing edge 60 such that pressure and suction-side walls 54, 56can be said to extend in chord or chordwise between the leading edge 58and the trailing edge 60.

The airfoil 52 includes a root or first end 64 which intersects with andextends radially outwardly from a base or platform 66 of the turbinerotor blade 50. The airfoil 52 terminates radially at a second end orradial tip 68 of the airfoil 52. The pressure and suction-side walls 54,56 can be said to extend in span or in a span-wise direction 70 betweenthe root 64 and/or the platform 66 and the radial tip 68 of the airfoil52. In other words, each turbine rotor blade 50 includes an airfoil 52having opposing pressure and suction-side walls 54, 56 that extend inchord or chordwise 62 between opposing leading and trailing edges 58, 60and that extend in span or span-wise 70 between the root 64 and theradial tip 68 of the airfoil 52.

In particular configurations, the airfoil 52 may include a fillet 72formed between the platform 66 and the airfoil 52 proximate to the root64. The fillet 72 can include a weld or braze fillet, which can beformed via conventional MIG welding, TIG welding, brazing, etc., and caninclude a profile that can reduce fluid dynamic losses as a result ofthe presence of fillet 72. In particular embodiments, the platform 66,airfoil 52 and the fillet 72 can be formed as a single component, suchas by casting and/or machining and/or 3D printing and/or any othersuitable technique now known or later developed and/or discovered. Inparticular configurations, the turbine rotor blade 50 includes amounting portion 74 which is formed to connect and/or to secure theturbine rotor blade 50 to the rotor shaft 14.

The airfoil 52 of the turbine rotor blade 50 has a profile at anycross-section taken between the platform 66 or the root 64 and theradial tip 68. The X, Y, and Z values are given in Table I as percentagevalues of the airfoil length or height/span. As one example only, theheight or radial span of the airfoil 52 of turbine rotor blade 50 may befrom about 5 inches to about 20 inches. However, it is to be understoodthat heights below or above this range may also be employed as desiredin the specific application.

A gas turbine hot gas path requires airfoils that meet systemrequirements of aerodynamic and mechanical blade loading and efficiency.To define the airfoil shape of each turbine rotor blade airfoil, thereis a unique set or loci of points in space that meet the stagerequirements and that can be manufactured. This unique loci of pointsmeets the requirements for stage efficiency and are arrived at byiteration between aerodynamic and mechanical loadings enabling theturbine to run in an efficient, safe and smooth manner. These points areunique and specific to the system and are not obvious to those skilledin the art.

The loci which defines the airfoil profile of turbine rotor blade 50comprises a set of about 2,200 points with X, Y and Z dimensionsrelative to a reference origin coordinate system. The Cartesiancoordinate system of X, Y and Z values given in Table I below definesthe airfoil profile of the turbine rotor blade 50 at various locationsalong its length and height or radial span. Table I lists data for anon-coated airfoil, and the envelope/tolerance for the coordinates isabout +/−5% in a direction normal to any airfoil surface location. Apoint data origin 76 is defined at or proximate to the root 64 at theleading edge 58. In one embodiment as presented in Table I below, thepoint data origin 76 is defined at or proximate to (above or below) atransition or intersection line 78 defined between the fillet 72 and theairfoil 52. The point data origin 76 corresponds to the non-dimensionalZ value of Table I (presented below) at Z equals 0.

The coordinate values for the X, Y and Z coordinates are set forth innon-dimensionalized units by the airfoil height in Table I althoughother units of dimensions may be used when the values are appropriatelyconverted. The X, Y, and Z values set forth in Table I are alsoexpressed in non-dimensional form (X, Y, and Z) from 0% to 100% of theairfoil 52 height or radial span 70. To convert the Z value to a Zcoordinate value, e.g., in inches, the non-dimensional Z value given inTable I is multiplied by the Z length of the airfoil in inches. Asdescribed above, the Cartesian coordinate system hasorthogonally-related X, Y and Z axes and the X axis lies generallyparallel to a centerline of the rotor shaft 14, i.e., the rotary axisand a positive X coordinate value is axial toward an aft, i.e., exhaustend of the turbine 10. The positive Y coordinate value extendstangentially in the direction of rotation of the rotor and the positiveZ coordinate value is radially outwardly toward the radial tip 68. Allthe values in Table I are given at room temperature and do not includethe fillet 72.

By defining X and Y coordinate values at selected locations in a Zdirection normal to the X, Y plane, the profile section or airfoil shapeof the airfoil 52 of the turbine rotor blade 50, at each Z distancealong the length of the airfoil 52 can be ascertained. By connecting theX and Y values with smooth continuing arcs, each profile section at eachdistance Z is fixed. The airfoil profiles of the various surfacelocations between the distances Z are determined by smoothly connectingthe adjacent profile sections to one another to form the airfoilprofile.

The Table I values are generated and shown to four decimal places fordetermining the profile of the airfoil 52. As the turbine rotor blade 50heats up during operation of the gas turbine 12, surface stress andtemperature will cause a change in the X, Y and Z's. Accordingly, thevalues for the profile given in Table I represent ambient, non-operatingor non-hot conditions (e.g., room temperature) and are for an uncoatedairfoil.

There are typical manufacturing tolerances as well as coatings whichmust be accounted for in the actual profile of the airfoil 52. Eachcross-section is joined smoothly with the other cross-sections to formthe complete airfoil shape. It will therefore be appreciated that +/−typical manufacturing tolerances, i.e., +/− values, including anycoating thicknesses, are additive to the X and Y values given in Table Ibelow. Accordingly, a distance of +/−5% in a direction normal to anysurface location along the airfoil profile defines an airfoil profileenvelope for this particular turbine rotor blade 50 airfoil design andturbine 12, i.e., a range of variation between measured points on theactual airfoil surface at nominal cold or room temperature and the idealposition of those points as given in Table I below at the sametemperature. The data provided in Table I is scalable and the geometrypertains to all aerodynamic scales, at, above and/or below a 3000-3600RPM range. The design of the airfoil 52 for turbine rotor blade 50 isrobust to this range of variation without impairment of mechanical andaerodynamic functions.

TABLE I SUCTION-SIDE PRESSURE-SIDE X (%) Y (%) Z (%) N X (%) Y (%) Z (%)0.0000 0.0000 0.0000 1 0.0000 0.0000 0.0000 −0.6179 0.9061 0.0000 20.6206 −0.3865 0.0000 −0.8829 1.9769 0.0000 3 1.3301 −0.5682 0.0000−0.9152 3.0815 0.0000 4 2.0634 −0.5851 0.0000 −0.7952 4.1807 0.0000 52.7924 −0.4976 0.0000 −0.5743 5.2645 0.0000 6 3.5131 −0.3556 0.0000−0.2815 6.3313 0.0000 7 4.2279 −0.1862 0.0000 0.0680 7.3809 0.0000 84.9385 −0.0002 0.0000 0.4649 8.4135 0.0000 9 5.6456 0.1989 0.0000 0.90199.4299 0.0000 10 6.3495 0.4091 0.0000 1.3731 10.4309 0.0000 11 7.05060.6284 0.0000 1.8738 11.4174 0.0000 12 7.7493 0.8551 0.0000 2.400712.3902 0.0000 13 8.4460 1.0878 0.0000 2.9513 13.3498 0.0000 14 9.14121.3251 0.0000 3.5239 14.2965 0.0000 15 9.8353 1.5657 0.0000 4.117615.2300 0.0000 16 10.5287 1.8083 0.0000 4.7319 16.1502 0.0000 17 11.22172.0519 0.0000 5.3669 17.0561 0.0000 18 11.9149 2.2951 0.0000 6.023117.9469 0.0000 19 12.6085 2.5370 0.0000 6.7007 18.8214 0.0000 20 13.30302.7764 0.0000 7.4006 19.6782 0.0000 21 13.9987 3.0122 0.0000 8.123220.5160 0.0000 22 14.6959 3.2434 0.0000 8.8692 21.3330 0.0000 23 15.39503.4690 0.0000 9.6390 22.1275 0.0000 24 16.0962 3.6879 0.0000 10.433322.8977 0.0000 25 16.7998 3.8992 0.0000 11.2524 23.6413 0.0000 2617.5059 4.1018 0.0000 12.0968 24.3561 0.0000 27 18.2147 4.2947 0.000012.9669 25.0393 0.0000 28 18.9263 4.4769 0.0000 13.8630 25.6881 0.000029 19.6409 4.6473 0.0000 14.7850 26.2994 0.0000 30 20.3583 4.8050 0.000015.7329 26.8699 0.0000 31 21.0786 4.9489 0.0000 16.7060 27.3960 0.000032 21.8018 5.0780 0.0000 17.7035 27.8743 0.0000 33 22.5276 5.1912 0.000018.7242 28.3010 0.0000 34 23.2558 5.2874 0.0000 19.7662 28.6724 0.000035 23.9862 5.3658 0.0000 20.8273 28.9850 0.0000 36 24.7184 5.4254 0.000021.9048 29.2354 0.0000 37 25.4519 5.4653 0.0000 22.9954 29.4204 0.000038 26.1862 5.4848 0.0000 24.0954 29.5377 0.0000 39 26.9207 5.4830 0.000025.2005 29.5860 0.0000 40 27.6549 5.4596 0.0000 26.3065 29.5649 0.000041 28.3880 5.4138 0.0000 27.4090 29.4749 0.0000 42 29.1194 5.3454 0.000028.5039 29.3169 0.0000 43 29.8483 5.2542 0.0000 29.5871 29.0926 0.000044 30.5739 5.1399 0.0000 30.6551 28.8042 0.0000 45 31.2955 5.0026 0.000031.7047 28.4548 0.0000 46 32.0124 4.8425 0.0000 32.7333 28.0478 0.000047 32.7239 4.6597 0.0000 33.7391 27.5873 0.0000 48 33.4292 4.4547 0.000034.7207 27.0770 0.0000 49 34.1279 4.2278 0.0000 35.6768 26.5204 0.000050 34.8193 3.9796 0.0000 36.6065 25.9208 0.0000 51 35.5029 3.7108 0.000037.5090 25.2811 0.0000 52 36.1783 3.4220 0.0000 38.3839 24.6040 0.000053 36.8451 3.1139 0.0000 39.2307 23.8920 0.0000 54 37.5031 2.7873 0.000040.0493 23.1479 0.0000 55 38.1519 2.4430 0.0000 40.8400 22.3741 0.000056 38.7915 2.0817 0.0000 41.6029 21.5729 0.0000 57 39.4217 1.7042 0.000042.3388 20.7468 0.0000 58 40.0424 1.3113 0.0000 43.0483 19.8979 0.000059 40.6536 0.9038 0.0000 43.7324 19.0285 0.0000 60 41.2553 0.4825 0.000044.3922 18.1405 0.0000 61 41.8475 0.0479 0.0000 45.0290 17.2358 0.000062 42.4304 −0.3991 0.0000 45.6442 16.3162 0.0000 63 43.0040 −0.85800.0000 46.2391 15.3834 0.0000 64 43.5685 −1.3281 0.0000 46.8151 14.43890.0000 65 44.1239 −1.8088 0.0000 47.3736 13.4838 0.0000 66 44.6704−2.2997 0.0000 47.9159 12.5195 0.0000 67 45.2081 −2.8002 0.0000 48.443111.5468 0.0000 68 45.7372 −3.3098 0.0000 48.9562 10.5666 0.0000 6946.2577 −3.8281 0.0000 49.4560 9.5796 0.0000 70 46.7698 −4.3548 0.000049.9434 8.5864 0.0000 71 47.2735 −4.8894 0.0000 50.4191 7.5875 0.0000 7247.7690 −5.4318 0.0000 50.8837 6.5834 0.0000 73 48.2563 −5.9814 0.000051.3377 5.5745 0.0000 74 48.7357 −6.5381 0.0000 51.7816 4.5611 0.0000 7549.2071 −7.1014 0.0000 52.2159 3.5435 0.0000 76 49.6710 −7.6710 0.000052.6410 2.5221 0.0000 77 50.1274 −8.2466 0.0000 53.0574 1.4970 0.0000 7850.5766 −8.8278 0.0000 53.4654 0.4687 0.0000 79 51.0189 −9.4143 0.000053.8656 −0.5628 0.0000 80 51.4546 −10.0057 0.0000 54.2585 −1.5970 0.000081 51.8838 −10.6019 0.0000 54.6447 −2.6338 0.0000 82 52.3068 −11.20250.0000 55.0246 −3.6729 0.0000 83 52.7237 −11.8073 0.0000 55.3990 −4.71400.0000 84 53.1346 −12.4162 0.0000 55.7684 −5.7569 0.0000 85 53.5398−13.0289 0.0000 56.1332 −6.8014 0.0000 86 53.9393 −13.6454 0.000056.4939 −7.8473 0.0000 87 54.3333 −14.2654 0.0000 56.8505 −8.8946 0.000088 54.7219 −14.8888 0.0000 57.2033 −9.9432 0.0000 89 55.1051 −15.51550.0000 57.5523 −10.9931 0.0000 90 55.4831 −16.1454 0.0000 57.8974−12.0443 0.0000 91 55.8558 −16.7784 0.0000 58.2386 −13.0967 0.0000 9256.2234 −17.4144 0.0000 58.5756 −14.1505 0.0000 93 56.5859 −18.05330.0000 58.9084 −15.2057 0.0000 94 56.9434 −18.6950 0.0000 59.2367−16.2622 0.0000 95 57.2961 −19.3394 0.0000 59.5605 −17.3201 0.0000 9657.6440 −19.9864 0.0000 59.8795 −18.3795 0.0000 97 57.9873 −20.63580.0000 60.1937 −19.4403 0.0000 98 58.3934 −21.2417 0.0000 60.3912−20.5182 0.0000 99 59.0573 −21.5273 0.0000 59.7670 −21.3847 0.0000 10059.7670 −21.3847 0.0000 0.3825 0.6250 10.0000 1 0.3825 0.6250 10.0000−0.0778 1.6429 10.0000 2 0.9061 0.1018 10.0000 −0.2488 2.7510 10.0000 31.5774 −0.2104 10.0000 −0.2388 3.8733 10.0000 4 2.3117 −0.3153 10.0000−0.1077 4.9884 10.0000 5 3.0526 −0.2593 10.0000 0.1107 6.0899 10.0000 63.7837 −0.1235 10.0000 0.3963 7.1760 10.0000 7 4.5074 0.0485 10.00000.7360 8.2464 10.0000 8 5.2263 0.2394 10.0000 1.1207 9.3015 10.0000 95.9420 0.4417 10.0000 1.5441 10.3418 10.0000 10 6.6551 0.6533 10.00002.0017 11.3674 10.0000 11 7.3655 0.8739 10.0000 2.4901 12.3788 10.000012 8.0732 1.1028 10.0000 3.0065 13.3761 10.0000 13 8.7784 1.3392 10.00003.5487 14.3597 10.0000 14 9.4817 1.5816 10.0000 4.1148 15.3297 10.000015 10.1832 1.8287 10.0000 4.7034 16.2862 10.0000 16 10.8837 2.078910.0000 5.3140 17.2289 10.0000 17 11.5836 2.3306 10.0000 5.9467 18.156810.0000 18 12.2835 2.5827 10.0000 6.6019 19.0690 10.0000 19 12.98362.8337 10.0000 7.2802 19.9641 10.0000 20 13.6846 3.0826 10.0000 7.982420.8407 10.0000 21 14.3866 3.3283 10.0000 8.7091 21.6970 10.0000 2215.0901 3.5700 10.0000 9.4610 22.5313 10.0000 23 15.7953 3.8065 10.000010.2387 23.3415 10.0000 24 16.5026 4.0369 10.0000 11.0428 24.125510.0000 25 17.2122 4.2599 10.0000 11.8740 24.8808 10.0000 26 17.92444.4743 10.0000 12.7327 25.6046 10.0000 27 18.6396 4.6787 10.0000 13.619326.2940 10.0000 28 19.3579 4.8717 10.0000 14.5340 26.9457 10.0000 2920.0795 5.0523 10.0000 15.4766 27.5562 10.0000 30 20.8043 5.2191 10.000016.4469 28.1217 10.0000 31 21.5324 5.3714 10.0000 17.4441 28.638110.0000 32 22.2636 5.5080 10.0000 18.4672 29.1011 10.0000 33 22.99775.6277 10.0000 19.5144 29.5066 10.0000 34 23.7345 5.7291 10.0000 20.583529.8505 10.0000 35 24.4738 5.8110 10.0000 21.6715 30.1285 10.0000 3625.2150 5.8724 10.0000 22.7749 30.3370 10.0000 37 25.9578 5.9122 10.000023.8895 30.4738 10.0000 38 26.7014 5.9296 10.0000 25.0106 30.536710.0000 39 27.4451 5.9240 10.0000 26.1335 30.5238 10.0000 40 28.18835.8944 10.0000 27.2530 30.4357 10.0000 41 28.9301 5.8403 10.0000 28.364230.2742 10.0000 42 29.6697 5.7614 10.0000 29.4627 30.0408 10.0000 4330.4062 5.6575 10.0000 30.5440 29.7380 10.0000 44 31.1387 5.5286 10.000031.6050 29.3699 10.0000 45 31.8664 5.3745 10.0000 32.6428 28.941010.0000 46 32.5883 5.1956 10.0000 33.6553 28.4552 10.0000 47 33.30384.9922 10.0000 34.6408 27.9167 10.0000 48 34.0120 4.7648 10.0000 35.598427.3299 10.0000 49 34.7122 4.5140 10.0000 36.5275 26.6991 10.0000 5035.4040 4.2407 10.0000 37.4281 26.0281 10.0000 51 36.0867 3.9457 10.000038.3003 25.3206 10.0000 52 36.7601 3.6297 10.0000 39.1442 24.579610.0000 53 37.4237 3.2938 10.0000 39.9606 23.8083 10.0000 54 38.07732.9388 10.0000 40.7498 23.0093 10.0000 55 38.7207 2.5655 10.0000 41.512722.1850 10.0000 56 39.3537 2.1750 10.0000 42.2499 21.3378 10.0000 5739.9763 1.7680 10.0000 42.9621 20.4694 10.0000 58 40.5884 1.3456 10.000043.6502 19.5817 10.0000 59 41.1903 0.9085 10.0000 44.3150 18.676510.0000 60 41.7818 0.4576 10.0000 44.9574 17.7553 10.0000 61 42.3633−0.0063 10.0000 45.5784 16.8195 10.0000 62 42.9348 −0.4823 10.000046.1792 15.8705 10.0000 63 43.4965 −0.9699 10.0000 46.7606 14.909610.0000 64 44.0487 −1.4683 10.0000 47.3236 13.9378 10.0000 65 44.5914−1.9769 10.0000 47.8694 12.9562 10.0000 66 45.1249 −2.4952 10.000048.3989 11.9657 10.0000 67 45.6494 −3.0226 10.0000 48.9130 10.967110.0000 68 46.1650 −3.5587 10.0000 49.4126 9.9612 10.0000 69 46.6718−4.1031 10.0000 49.8987 8.9487 10.0000 70 47.1700 −4.6554 10.000050.3721 7.9302 10.0000 71 47.6598 −5.2153 10.0000 50.8334 6.9062 10.000072 48.1411 −5.7824 10.0000 51.2836 5.8772 10.0000 73 48.6141 −6.356410.0000 51.7232 4.8437 10.0000 74 49.0790 −6.9370 10.0000 52.1529 3.806010.0000 75 49.5360 −7.5239 10.0000 52.5733 2.7645 10.0000 76 49.9852−8.1168 10.0000 52.9850 1.7196 10.0000 77 50.4269 −8.7153 10.000053.3885 0.6714 10.0000 78 50.8614 −9.3190 10.0000 53.7841 −0.379810.0000 79 51.2891 −9.9276 10.0000 54.1720 −1.4338 10.0000 80 51.7100−10.5408 10.0000 54.5525 −2.4905 10.0000 81 52.1246 −11.1584 10.000054.9259 −3.5498 10.0000 82 52.5328 −11.7802 10.0000 55.2927 −4.611310.0000 83 52.9349 −12.4059 10.0000 55.6539 −5.6748 10.0000 84 53.3309−13.0355 10.0000 56.0103 −6.7399 10.0000 85 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100.0000 44 34.3295 10.0067 100.0000 40.910528.6557 100.0000 45 34.8871 9.4862 100.0000 41.5930 27.8625 100.0000 4635.4334 8.9538 100.0000 42.2414 27.0412 100.0000 47 35.9688 8.4104100.0000 42.8570 26.1951 100.0000 48 36.4936 7.8568 100.0000 43.441725.3272 100.0000 49 37.0082 7.2938 100.0000 43.9975 24.4406 100.0000 5037.5130 6.7219 100.0000 44.5266 23.5377 100.0000 51 38.0085 6.1419100.0000 45.0311 22.6210 100.0000 52 38.4949 5.5544 100.0000 45.513321.6922 100.0000 53 38.9728 4.9598 100.0000 45.9750 20.7531 100.0000 5439.4425 4.3587 100.0000 46.4180 19.8051 100.0000 55 39.9043 3.7516100.0000 46.8439 18.8492 100.0000 56 40.3586 3.1388 100.0000 47.254017.8864 100.0000 57 40.8058 2.5209 100.0000 47.6496 16.9176 100.0000 5841.2463 1.8981 100.0000 48.0318 15.9435 100.0000 59 41.6803 1.2708100.0000 48.4018 14.9646 100.0000 60 42.1082 0.6393 100.0000 48.760413.9815 100.0000 61 42.5302 0.0038 100.0000 49.1085 12.9946 100.0000 6242.9466 −0.6353 100.0000 49.4469 12.0044 100.0000 63 43.3577 −1.2779100.0000 49.7763 11.0111 100.0000 64 43.7636 −1.9237 100.0000 50.097310.0151 100.0000 65 44.1647 −2.5725 100.0000 50.4106 9.0166 100.0000 6644.5611 −3.2243 100.0000 50.7165 8.0159 100.0000 67 44.9530 −3.8787100.0000 51.0156 7.0131 100.0000 68 45.3405 −4.5357 100.0000 51.30836.0083 100.0000 69 45.7240 −5.1952 100.0000 51.5948 5.0018 100.0000 7046.1034 −5.8569 100.0000 51.8754 3.9937 100.0000 71 46.4790 −6.5209100.0000 52.1504 2.9840 100.0000 72 46.8509 −7.1869 100.0000 52.42011.9729 100.0000 73 47.2193 −7.8548 100.0000 52.6845 0.9604 100.0000 7447.5845 −8.5246 100.0000 52.9439 −0.0534 100.0000 75 47.9465 −9.1960100.0000 53.1983 −1.0685 100.0000 76 48.3055 −9.8690 100.0000 53.4479−2.0848 100.0000 77 48.6618 −10.5435 100.0000 53.6929 −3.1022 100.000078 49.0155 −11.2194 100.0000 53.9332 −4.1207 100.0000 79 49.3670−11.8964 100.0000 54.1691 −5.1402 100.0000 80 49.7163 −12.5745 100.000054.4007 −6.1607 100.0000 81 50.0638 −13.2536 100.0000 54.6281 −7.1822100.0000 82 50.4097 −13.9335 100.0000 54.8514 −8.2045 100.0000 8350.7541 −14.6141 100.0000 55.0710 −9.2277 100.0000 84 51.0973 −15.2953100.0000 55.2869 −10.2517 100.0000 85 51.4395 −15.9771 100.0000 55.4994−11.2764 100.0000 86 51.7808 −16.6593 100.0000 55.7089 −12.3016 100.000087 52.1215 −17.3418 100.0000 55.9156 −13.3275 100.0000 88 52.4616−18.0246 100.0000 56.1196 −14.3539 100.0000 89 52.8013 −18.7076 100.000056.3213 −15.3807 100.0000 90 53.1409 −19.3907 100.0000 56.5203 −16.4081100.0000 91 53.4804 −20.0737 100.0000 56.7166 −17.4360 100.0000 9253.8200 −20.7568 100.0000 56.9094 −18.4645 100.0000 93 54.1599 −21.4397100.0000 57.0981 −19.4939 100.0000 94 54.5002 −22.1224 100.0000 57.2814−20.5242 100.0000 95 54.8412 −22.8047 100.0000 57.4584 −21.5556 100.000096 55.1830 −23.4867 100.0000 57.6287 −22.5881 100.0000 97 55.5258−24.1681 100.0000 57.7925 −23.6216 100.0000 98 55.8699 −24.8489 100.000057.8558 −24.6566 100.0000 99 56.4085 −25.3585 100.0000 57.1555 −25.3786100.0000 100 57.1555 −25.3786 100.0000

It will also be appreciated that the airfoil 52 disclosed in the aboveTable I may be scaled up or down geometrically for use in other similarturbine designs. Consequently, the coordinate values set forth in TableI may be scaled upwardly or downwardly such that the airfoil profileshape remains unchanged. A scaled version of the coordinates in Table Iwould be represented by X, Y and Z coordinate values of Table I, withthe X, Y and Z non-dimensional coordinate values converted to inches,multiplied or divided by a constant number.

An important term in this disclosure is “profile”. The profile is therange of the variation between measured points on an airfoil surface andthe ideal position listed in Table I. The actual profile on amanufactured turbine rotor blade will be different than those in Table Iand the design is robust to this variation meaning that mechanical andaerodynamic function are not impaired. As noted above, a + or −5%profile tolerance is used herein. The X, Y and Z values are allnon-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to the machineconditions and specifications. It provides a unique profile toachieve 1) interaction between other stages in the turbine 10; 2)aerodynamic efficiency; and 3) normalized aerodynamic and mechanicalblade loadings. The disclosed loci of points defined in Table I allowthe gas turbine 12 or any other suitable turbine to run in an efficient,safe and smooth manner. As also noted, any scale of the disclosedairfoil 52 may be adopted as long as 1) interaction between other stagesin the pressure turbine 10; 2) aerodynamic efficiency; and 3) normalizedaerodynamic and mechanical blade loadings are maintained in the scaledturbine.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined by the claims, and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims if they have structural elementsthat do not differ from the literal language of the claims, or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal languages of the claims.

What is claimed is:
 1. A turbine rotor blade including an airfoil havingan airfoil shape, the airfoil having a nominal profile substantially inaccordance with Cartesian coordinate values of X, Y and Z set forth inTable I, wherein the Cartesian coordinate values of X, Y and Z arenon-dimensional values from 0% to 100% convertible to dimensionaldistances in inches by multiplying the Cartesian coordinate values of X,Y and Z by a height of the airfoil in inches, and wherein X and Y aredistances in inches which, when connected by smooth continuing arcs,define airfoil profile sections at each distance Z, the airfoil profilesections at Z distances being joined smoothly with one another to form acomplete airfoil shape.
 2. The turbine rotor blade as in claim 1,forming part of a stage of a turbine.
 3. The turbine rotor blade as inclaim 1, wherein the turbine rotor blade forms a part of a first stageof turbine rotor blades of a turbine of a gas turbine.
 4. The turbinerotor blade as in claim 1, wherein the airfoil shape lies in an envelopewithin +/−5% in a direction normal to any airfoil surface location. 5.The turbine rotor blade as in claim 1, wherein a height of the turbinerotor blade is 5 inches to 20 inches.
 6. A turbine rotor blade includingan airfoil having a suction-side uncoated nominal airfoil profilesubstantially in accordance with suction-side Cartesian coordinatevalues of X, Y and Z set forth in Table I, wherein the Cartesiancoordinate values of X, Y and Z are non-dimensional values from 0% to100% convertible to dimensional distances in inches by multiplying theCartesian coordinate values of X, Y and Z by a height of the airfoil ininches, and wherein X and Y are distances in inches which, whenconnected by smooth continuing arcs, define airfoil profile sections ateach Z distance, the airfoil profile sections at the Z distances beingjoined smoothly with one another to form a complete suction-side airfoilshape, the X, Y and Z distances being scalable as a function of the sameconstant or number to provide a scaled-up or scaled-down airfoil.
 7. Theturbine rotor blade as in claim 6, forming part of a stage of a turbine.8. The turbine rotor blade as in claim 6, wherein the turbine rotorblade forms a part of a first stage of turbine rotor blades of a turbineof a gas turbine.
 9. The turbine rotor blade as in claim 6, wherein thesuction-side airfoil shape lies in an envelope within +/−5% in adirection normal to any suction-side airfoil surface location.
 10. Theturbine rotor blade as in claim 6, wherein a height of the turbine rotorblade is about 5 inches to about 20 inches.
 11. A turbine comprising aturbine wheel having a plurality of turbine rotor blades, each of theturbine rotor blades including an airfoil having a suction-side airfoilshape, the airfoil having a nominal profile substantially in accordancewith suction-side Cartesian coordinate values of X, Y and Z set forth inTable I wherein the Cartesian coordinate values of X, Y and Z arenon-dimensional values from 0% to 100% convertible to dimensionaldistances by multiplying the Cartesian coordinate values of X, Y and Zby a height of the airfoil, and wherein X and Y are distances which,when connected by smooth continuing arcs, define airfoil profilesections at each Z distance, the airfoil profile sections at the Zdistances being joined smoothly with one another to form a completesuction-side airfoil shape.
 12. The turbine as in claim 11, wherein theturbine rotor blade is a first stage turbine rotor blade.
 13. Theturbine as in claim 11, wherein X represents a distance parallel to theturbine axis of rotation.
 14. The turbine as in claim 11, wherein thesuction-side airfoil shape lies in an envelope within +/−5% in adirection normal to any suction-side airfoil surface location.
 15. Theturbine as in claim 11, wherein a height of the turbine rotor blade isabout 5 inches to about 20 inches.
 16. The turbine as in claim 11,wherein each of the turbine rotor blades includes an airfoil having apressure-side airfoil shape, the airfoil having a nominal profilesubstantially in accordance with pressure-side Cartesian coordinatevalues of X, Y and Z set forth in Table I wherein the pressure-sideCartesian coordinate values of X, Y and Z are non-dimensional valuesfrom 0% to 100% convertible to dimensional distances by multiplying thepressure-side Cartesian coordinate values of X, Y and Z by a height ofthe airfoil, and wherein X and Y are distances which, when connected bysmooth continuing arcs, define airfoil profile sections at each Zdistance, the airfoil profile sections at Z distances being joinedsmoothly with one another to form a complete airfoil shape.
 17. Theturbine as in claim 16, wherein the turbine rotor blade is a first stageturbine rotor blade.
 18. The turbine as in claim 14, wherein Xrepresents a distance parallel to the turbine axis of rotation.
 19. Theturbine as in claim 16, wherein the airfoil shape lies in an envelopewithin +/−5% in a direction normal to any airfoil surface location. 20.The turbine as in claim 16, wherein a height of the turbine rotor bladeis about 5 inches to about 20 inches.